Question

solve the differential eqn, dy/dx=xsquared-ysquared all over xy.

Answer 1

\[\frac{\text dy}{\text dx}=\frac{x^2-y^2}{xy}\]

Answer 2

You should try and separate the variables, y's on one side of the equal sign, x's on the other.

Answer 3

divine the numerator and denominator by x^2,
you will now have a Homogenous equation

Answer 4

then substitute \(v=\frac yx\)

Answer 5

\[y=vx\]\[\frac {\text dy}{\text dx}=x\frac {\text dv}{\text dx}+v\]

Answer 6

\[\frac{\text dy}{\text dx}=\frac{x^2-y^2}{xy}=\frac{1-\left(\frac yx\right)^2}{\frac yx}\]
\[x\frac{\text dv}{\text dx}+v=\frac{1-v^2}{v}\]